Let T: R³ → R³ be a linear operator and B = [v₁, V2, V3] a basis for R³. Suppose 0 T(v₁) =_=A T(v₂): T (V3) = [33] i. Determine whether w = -- 0 ii. Find a bases for R(T) iii. Find dim (N(T)) is in the range of T

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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Question
3.
Let T: R³ R³ be a linear operator and B = [V₁, V2, V3] a basis for R³. Suppose
TOD-_TO-A_TO-7
T(v₁)
=
T(v₂) =
T(v3) =
0
6]
i.
Determine whether w =
5 is in the range of T
0
ii.
Find a bases for R(T)
iii.
Find dim (N(T))
Transcribed Image Text:3. Let T: R³ R³ be a linear operator and B = [V₁, V2, V3] a basis for R³. Suppose TOD-_TO-A_TO-7 T(v₁) = T(v₂) = T(v3) = 0 6] i. Determine whether w = 5 is in the range of T 0 ii. Find a bases for R(T) iii. Find dim (N(T))
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